## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 40, Number 3 (1969), 953-969.

### Upper and Lower Probability Inferences for Families of Hypotheses with Monotone Density Ratios

#### Abstract

Models of the second kind, described in Section 2, are applied to define inferences about single parameter families having monotone density ratio structure. A definition and some properties of this structure are given in Section 3 along with basic general formulas for inferences. Mixture families always have the monotone density ratio property, and some theory and illustrations are given in Section 4. Location and scale parameter families sometimes have the property, as shown and illustrated in Section 5 where the examples consist of uniform and normal location parameters and exponential and normal scale parameters.

#### Article information

**Source**

Ann. Math. Statist., Volume 40, Number 3 (1969), 953-969.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177697600

**Digital Object Identifier**

doi:10.1214/aoms/1177697600

**Mathematical Reviews number (MathSciNet)**

MR246427

**Zentralblatt MATH identifier**

0211.50204

**JSTOR**

links.jstor.org

#### Citation

Dempster, A. P. Upper and Lower Probability Inferences for Families of Hypotheses with Monotone Density Ratios. Ann. Math. Statist. 40 (1969), no. 3, 953--969. doi:10.1214/aoms/1177697600. https://projecteuclid.org/euclid.aoms/1177697600